Dimensions: A Walk Through Mathematics
A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed!
Dimension Two - Hipparchus shows us how to describe the position of any point on Earth with two numbers... and explains the stereographic projection: how to draw a map of the world.
Dimension Three - M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.
The Fourth Dimension - Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension... and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces!
Complex Numbers - Mathematician Adrien Douady explains complex numbers. The square root of negative numbers made easy! Transforming the plane, deforming images, creating fractal images...
Fibration - Mathematician Heinz Hopf explains his "fibration". Using complex numbers he constructs pretty patterns of circles in space. Circles, tori... everything rotating in four-dimensional space.
Proof - Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem concerning the stereographic projection. Support the authors and buy the DVD here.
@iraoksman
What is to say that the sum of the angles of all dimension "must" be 4x90 degrees in a fourth dimension? Is this the influence of the three dimensional space we live in or...?
If a tesaract is a shadow of an object cast in 3 dimensional space from the 4th dimension, and rather than anything else, the light being disbursed is coming through a portal, what is the state of that portal influencing our recognition of space by studying a shadow?
What if the bridge is a Rosen-bridge and this Rosen-bridge is formed like an elliptic curve such described by Shimura-Tamiyama, is then the light source not really originating from ourselves and thus we have no outside dimensional awareness but that of our own shadows through a distortion of space.
Hmmmm
I think the concept of dimensional reasoning beyond our own frame of observation is quite unfinished. There may be more than one not followed road to the the understanding of this geometrical concept.
I highly value all attempting the journey but I feel at the same time there are to many non considered thoughts along its path.
Very very good. Excellent job. The graphics, the classical music, the soft slow deliberate tone, and meter of the explanations excellent work.
I can see some lucky children learning this essential knowledge, and thinking fondly of this video 30-40 years from now. Hopefully in a new world of peace, and tranquility.
dimention cero is a point
1st dimention is a point in movement, a line
2nd dimention is a line in movement, a surface
3rd dimention is a surface in movement, a volume
4th dimention is a computericed movement of 3rd dimention
so what
Maybe I'm doing my usual, over complicating, but if you live in flat land surely you have no horizon, how would you see the stereographic projections. Also silly with the cross sections, you could slice things any number of ways and get a different shape. The music is irritating and the man is too slow :)
Too much space between informormation...speed it up x1.5 and its proper
i see 3d in different shapes, or 1thats without imagination but i still cant see or imagine 4d? what differentiates 3d between 4d?
If you live in flatland, how do you observe an object of any SHAPE, if your line of sight is limited to, left/right, forwards/backwards? Is it possible you only see a line representing the width of the object at the time it passes through flatland. I assume from representations of people like Carl Sagan & Lois De Broy that there is no observational up and down in flatland, suggesting the only way to see shapes in flatland is by observing them from from above or below. If you live in flatland, there is NO above OR below, because there is no up or down.
Best math lesson I ever got! I have to rewatch this to understand what the 4th dimension is. All the examples of 4d objects looked 3d... which I think is the point...since we can't see in 4d... but then what's 4d and how can anyone explain it if humans only see in 2 dimensions? So many things to follow through on... great documentary.
At introduction I think: "of course another Euro-centric history of science." Why is it Westerners are so obsessed with 1. attributing all science to the Greek, while there is so much literature on science earlier and everywhere else on the globe 2. why they keep thinking they are the Greek's successor, while the Greeks themselves associated with Asia much more and abhorred Western "barbarians"?
I see your point in the 4d/3d, but when you think about it, it gets kind of freaky and mindblowing. I dont think it is possible to trick a persons mind to see another perpendicular axis no matter what technology you use, because that is what you would have to do...
Also when you think about if we were living in a 2-dimensional world, how should we then see the third dimension when the way we would look at the world was as if it had only 1 dimension?
When you think about it, we only see a plane of which we interpret in our minds in such way, that it is converted in to another, 3rd, dimension.
As i see it, it could only work, if we could see in 3 dimensions instead of only 2. This would require that we could watch all sides of an object simultaneously / what we are looking at.
Maybe if we had enough mind capacity, and the right configuration of our neural network, it would be possible to grasp the concept of actually having a model of an object in 3d, which might could lead to the individual persons understanding of a 4d object, but i consider that totally indigestible to the human mind. Can you see my point?
I do not really know anything about 3d technology, but i know for sure, that no technology alone could make us see in 4d afterall
(email censored)
brilliant documentary.
This has interrested me for a very long time. And I've never been able to really get my head around the subject.
I must say this documentary has given me renewed enthousiasm to try and 'see' in 4D :-)
What would really interrest me is seeing a 'shadow' of a 4D object built in 3D space. And then, using vanishing points (or planes ?) - similar to those we use to create the illusion of 3D on a 2D paper or screen - to create the illusion of 4D in the 3D space.
If Escher were still alive, he would surely be of great help in this area...
What we see in books and on the screen, is really a 2D object giving us the illusion of a 3D object using perspective. So we're always using the perspective trick to show 3D objects on a flat surface. Maybe losing the perspective and seeing in real 3D, and then using the perspective trick for the 4D to 3D downscaling would work.
Anyone know if this has been attempted/done yet ?
Are there any theories about 4D/3D vanishing points/planes ?
I think this 'projection' method of explanation is not compatible with my brain. I don't understand why we need to add in the extra layer of the sphere in order to project something onto a 2d surface and then do the same thing for 4d onto 3d, why not just project the actual shape instead of project the shape onto a sphere and then onto a something else. And where is Carl Sagan when you need him!
@hugs
that is an interesting take and i've heard it before.. I wonder what exactly you mean though.
I don't agree with all his arguments, but i believe his take on physics is dead on and i don't think he plays word games, he is just consistent with definitions and points out where people tend to misuse words or rather redefine them to fit their ideas with no regard to what the words actually mean.
i think he gets accused of that same as stefan molineux unfairly. there is no knowledge or communication without concrete definitions that don't get bent and twisted for convenience.
A good documentary film. Though, it requires full attention and a good mind for imagination. I really enjoy watching it just as much reading the comments given by all the smart guys.
@ Ren,
There is no maybe about it, our thoughts can and do move backwards in time and it's a skill that improves with age. Our thoughts can only move forward in time to speculate over very short periods of time by considering causality: as the fist comes swinging towards your face you know that in the short term future you will feel a stinging pain. Does that count as thoughts moving forward in time? I guess that it is still a speculation because one could dodge the blow or not, but as the time interval becomes smaller and smaller the speculation tends to fact. Lol.
By moving at FTL speeds it has been shown that a persons body can move forward in time. And yet as @Ren said it is physically impossible for us to move backwards in time. Are you still with me?
Thoughts can only move backwards and body can only move forwards in time.
When it comes to temporal quantum movement… Well, anything goes... It's like a zoo and the animals have all escaped from their cages... Bloody statistics, never give a straight answer to anything.
@ Ren, So in 5-D space all of the 3-D universe is just a point… Nice…
@princeton
That guy bgaede just plays word games. His arguments have more holes in them than Swiss cheese. They may 'sound' logical but are really full of illogical leaps.
I hesitate to post because until I press the button, there exist 42 posts, which I find amusing given the topic.
@ren
Here's a wacky thought. All spaces have subspaces, which I'll call borders and nodes. In 2D space, lines become borders and points become nodes. In 3D space a 2D space is a border between two 3D spaces and a line is a node or point of intersection between 2 or more borders. By analogy in 5D space, a 3D space becomes a node, analogous to a mere point.
All matter is really energy. Solid objects are a mere illusion. Energy is vibrating in all its possible dimensions. If for an instant a particle's vibrations in 3D are zero and increase in the fifth dimension, it could reappear anywhere in the 3D universe. Who's to say exactly how many dimensions our universe consists of or whether or not there are lower and higher dimensional universes? It's all an endlessly fascinating mindf--k.
One other thing. There seem to be alot of people struggling with the implications of E's TOR and it's implications for moving through time at or beyond the speed of light (Will I bump into myself climbing up the ladder in the past as I climb down in the present? etc.)
You people are needlessly torturing yourself. 10 years ago I was fascinated with the implcations of time. I read 3 books in a row purely on this subject to try and understand it better. All you need to know is this:
The 2nd Law of Thermodynamics states that entropy always increases (i.e it NEVER decreases). You don't even need to understand what this means (although it certainly would help you if you can be bothered doing a little reading on it). All you really need to understand is what this means - which is that time is and can ONLY ever be uni-directional. Time flows forward, always has and always will. It's impossible for it to do otherwise else it contradicts the 2nd Law. Therefore, entertaining notions about moving backwards in time is a pointless excercise - you can't resolve it in your mind because it was never possible in the first place, no matter how many Hollywood movies speculate about it being so (Back to the Future anyone? Lol).
If you really want to f@*k you head up though, it has been experimentally proven that the sub-atomic world is not subject to the limitation imposed by the speed of light. Information can (and does) move faster that the speed of light, and so do virual particles (VPs). VPs exist in pairs, but only exist 1 at a time (one exist now while the other half of the pair does not). Then one dissapears and the other simutaneously comes into existence, and each time this happens they exist at totally random points in the universe. They move around the universe like this in a way which is, again, not subject to the limit of the speed of light predicted by E's TOR. This is the essence of "Quantum Fluctuation". If there is a physical, rational explanation for the mechanics of consciousness and intuition, this is it. So the bottom line is, we cannot move backwards in time (or faster that we do), but maybe our thoughts can.
That's a mindf@*k (^-^).
Now where'd I put my weed...?
I note a few comments here from people who seem to be struggling to "picture" or "imagine" multiple dimensions.
Here's a litte help: you can't picture them - we live in a 3 dimensional space, so "picturing" higher timeframes is nigh on impossible with this as our only frame of reference. What you need to do is just understand their characteristics.
For example, picture a person or an object (i.e. a wooden block). It has height, length & width. Now imagine it moving through time - i.e. the block exists on Monday, Tuesday, Wednesday etc. You've just visualized a 4 dimensional object.
Higher dimensions work the same way - by adding an additional layer of complexity for each dimension. Imagine 3 blocks existing in 3 separate universes. That's 9 dimensions. Now imagine them all moving through the same Monday, Tuesday, Wednesday etc. That's 10 dimensions. Now imagine a string tied around all three universes containing the blocks as they move through time, with the string touching all three universes. That's 11 dimensions. Got it? Congratualations - you've just grasped the rudiments of modern string theory which predicts 11 dimensions (or 9 depending on the theoretical approach used).
Now you have two choices:
1) Go and do a degree in Maths so you can use & understand the tools that predict the theory or...
2) Sit back, smoke a huge joint and just think about it's implications (^_^).
Good luck!
wWOW very cool, 4d became much more conprehencable
had an experiance , a year ago, of turning my conciencensnes into a 4D structure and only now i finaly get it
This is one of the most mind boggling things I have ever came across. If anyone knows of any other docs on the subject that may give you a broader explanation.
i havent read all the posts, but hes talking about edges and vertices, that is discreet math and sounds like counting factorially to me
Picture all of these comments coming from those 2D lizards.
I think Its a good perspective of how we should urge ourselves to understand science.
There is some great information in this doc, but to be honest, as a doc, it's horrible. I had a hard time focusing because the animation is very very crude, the script is very unnatural sounding and the music is more distracting than not. I wish these people would have just made a video with people talking about the points without trying to incorporate a bunch of effects and aids they didn't know how to properly execute. - Would have been much more effective that way.
@princeton
There is only one of you. If you are traveling faster than the speed of light and see yourself as you move backwards then you are looking at what the real you has already done to get you to the place you are now to see you do it. Think of the ghosts of Christmas past. They are only shadows of what has been. You couldn't interact with them while you are traveling backwards in time as you would be interacting retroactively. If you stopped moving backwards and resumed progressing forward at Earth time then you could interact with yourself but only if your past self had already met your future self in the past which means you are going to meet yourself. This would create a time loop but only one since past you is going to become future you and future you is not going to replace past you. A self-correcting paradox could occur if your future self eliminated your past self and resumed his/her life from that point on but at each occurence your future self would be getting older and older until death which would be the correction.
There is a good book providing one possible view of time travel called "The Man Who Folded Himself" by David Gerrold. Though I don't think it actually represents true time travel it is an interesting read.